Critical behavior for mixed site-bond directed percolation

TL;DR

This study investigates the critical behavior of mixed site-bond directed percolation on 2D and 3D lattices using simulations, comparing results with theoretical bounds and an earlier isotropic percolation relationship.

Contribution

It provides a detailed analysis of critical fractions in mixed directed percolation and validates a known relationship for isotropic percolation in this context.

Findings

Critical fractions are well approximated by the isotropic percolation relationship.

Simulation results align closely with rigorous bounds.

The relationship holds across different lattice dimensions.

Abstract

We study mixed site-bond directed percolation on 2D and 3D lattices by using time-dependent simulations. Our results are compared with rigorous bounds recently obtained by Liggett and by Katori and Tsukahara. The critical fractions $p_{site}^c$ and $p_{bond}^c$ of sites and bonds are extremely well approximated by a relationship reported earlier for isotropic percolation, $(\log p_{site}^c/\log p_{site}^{c^*}+\log p_{bond}^c/\log p_{bond}^{c^*} = 1) $, where $p_{site}^{c^*}$ and $p_{bond}^{c^*}$ are the critical fractions in pure site and bond directed percolation.